1. FEA of Wind Turbine Tower Martin Knecht

2. The Problem FEA modeling of a wind turbine tower. Analysis: –Stress –Deflection Want to prevent –Yielding –Excessive deflection

3. Tower Construction Steel pipe –Diameter: 1.850 in. –Thickness: 0.225 in. –Length: 15 ft. Base –Pipe screewed into 5” flange. –Flange welded to 30” square, ¼ in. thick steel plate.

4. Tower Construction Bracket –Houses the permanent magnet alternator (PMA) –Six carbon fiber blades attached to PMA –Total weight of PMA, blades and bracket: 22.25 lb

5. Tower Construction Anchoring –Four ¼ inch steel cables –Breaking strength: 7000 lb –Attached 10 feet above the base of the tower (can not be attached higher due to blades) –Anchored 10 feet away from the base on the roof.

6. Tower Construction Purpose for FEA is safety: –Constructed around expensive equipment Solar panels Weather monitoring station –Constructed near edge of roof.

7. Loading and Conditions of Operation FEA modeled for high winds (60 and 100 mph) Constraints –Rigid constraint at base –Cables (“ropes”) Loads –Weight of PMA, blades and bracket: 22.25 lb –PMA torque –Wind drag

8. Loads PMA torque: –Torque due to PMA is negligible. With 33 mph winds it produces ~7.8e -4 lb-ft PMA stops generating power at high wind speeds as a safety factor –Not included in FEA Wind drag –Determined using the relationship: Drag = ½ C d r v 2 A air density = r = 1.2 kg/m 3 Wind speed = v = 60 and 100 mph Cross sectional area = A = 0.258 m 2 Coefficient of drag = C d ~ 1 –Drag at 60 mph = 25 lb –Drag at 100 mph = 70 lb

9. The FEA Model Pipe mesh –Split into three sections in order to mesh. –Each meshed separately –Needed to be aware of concentrated stresses at pipe boundaries. Fixed constraint on bottom of flange “Rope” constraints to model cables 1 ft

10. The FEA Model Loads applied to bracket at the top of pole. –Total body forces of 25 or 70 lb in x-direction to model the wind drag –Downward total body force of 22.3 lb to model the weigh of the turbine The weight should be offset from the bracket to more realistically model the distribution of mass of the turbine

11. The FEA Model Meshing –Would not mesh using h-adaptively if entire model was run at once. –Each pipe meshed separately and then assembled. Needed smaller mesh size at pipe boundaries, bracket-pipe boundary and flange-pipe boundary. Used loads with h-adaptively to force mesh sizes to be smaller where desired.

12. Results Deformations: –60 mph winds: Max. displacement: 2.36 in Location: Top of pole –100 mph wins: Max. displacement: 6.6 in Location: Top of pole –Note: Large deformations caused non-linear displacements of material.

13. Results Stresses at pipe-flange boundary –60 mph winds Stress: 1.2e8 Pa –100 mph winds Stress: 3.0e8 Pa –Yield stress of steel: 3.3e8 Pa At winds around 100 mph the structure will fail!

14. Improvements on Tower Model In order to reduce concentrated stresses and excessive deflections, the flange can be replaced by a spherical joint. Model was run using identical loads.

15. Improvements on Tower Model Deformations: –60 mph winds: Max. displacement: 0.25 in Location: Center of pole –100 mph wins: Max. displacement: 0.71 in Location: Center of pole

16. Improvements on Tower Model Stresses are distributed throughout entire pole with the joint Stresses at pipe-bracket boundary –60 mph winds Stress: 4.9e7 Pa Stresses reduced by a factor of 2.5 –100 mph winds Stress: 1.4e8 Pa Stresses reduces by a factor of 2 –Yield stress of steel: 3.3e8 Pa

17. If I had more time (and computing power)… More accurately distribute the weight of the turbine at the top of the tower. Model stresses on tower at different wind directions. Determine cable and anchor stresses. Consider dynamic loading modeling wind gusts. Determine vibrational resonances.